{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10-2 高斯的变分混合\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "    <img src=\"../pic/10_5.png\" width=\"200\" height=\"200\">\n",
    "</center>\n",
    "\n",
    "对于每个观测$x_n$,对应一个潜在变量$z_n$，为一个0,1组成的二值向量，元素为$z_{nk}$.$\\mathbf Z$的条件概率分布为\n",
    "$$p(\\mathbf Z|\\mathbf\\pi)=\\sum_{n=1}^N\\sum_{k=1}^N\\pi_{k}^{z_{nk}}$$\n",
    "观测数据向量的条件概率分布为:\n",
    "$$p(\\mathbf X|\\mathbf Z,\\mu,\\Lambda)=\\sum_{n=1}^N\\sum_{k=1}^K\\mathcal N(x_n|\\mu_k,\\Lambda_k^{-1})^{z_{nk}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "引入参数$\\mu,\\Lambda,\\pi$的先验概率分布，首先设混合系数$\\pi$的狄利克雷分布$$p(\\pi)=Dir(\\pi|\\alpha_0)=C(\\alpha_0)\\sum_{k=1}^K\\pi_k^{\\alpha_0-1}$$\n",
    "在引入高斯-Wishart先验分布，控制每个高斯分布的均值和精度\n",
    "$$\\begin{align}\n",
    "p(\\mu,\\Lambda)&=p(\\mu|\\Lambda)p(\\Lambda)\\\\&=\\sum_{k=1}^K\\mathcal N(\\mu_k|m_0(\\beta_0\\Lambda_k)^{-1}\\mathcal W(\\Lambda_k|W_0,\\nu_0)\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "所有变量的联合概率分布:\n",
    "$$p(X,Z,\\pi,\\mu,\\Lambda)=p(X|Z,\\mu,\\Lambda)p(Z|\\pi)p(\\pi)p(\\mu|\\Lambda)p(\\Lambda)$$\n",
    "我们现在考虑⼀个变分分布，它可以在潜在变量与参数之间进⾏分解:\n",
    "$$q(Z,\\pi,\\mu,\\Lambda)=q(Z)q(\\pi,\\mu,\\Lambda)$$\n",
    "更新方程为：\n",
    "$$lnq^*(Z)=\\mathbb E_{\\pi}[lnp(Z|\\pi)+\\mathbb E_{\\mu,\\Lambda}[lnp(X|Z,\\mu,\\Lambda)]+const$$\n",
    "第二个因子:\n",
    "$$lnq^*(\\pi,\\mu,\\Lambda)=lnp(\\pi)+\\sum_{k=1}^Klnp(\\mu_k,\\Lambda_k)+\\mathbb E_{Z}[lnp(Z|\\pi)]+\\sum_{k=1}^K\\sum_{n=1}^N\\mathbb E[z_{nk}]ln\\mathcal N(x_n|\\mu_k,\\Lambda_k^{-1})+const$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这个表达式的右侧分解成了若⼲项的和，⼀些项只与$\\pi$相关，⼀些项只与$\\mu$和$\\Lambda$相关，这说明变分后验概率可以进一步分解:\n",
    "$$q(\\pi,\\mu,\\Lambda)=q(\\pi)\\prod_{k=1}^Kq(\\mu_k,\\Lambda_k)$$\n",
    "\n",
    "分离出与$\\pi$有关的项，可以将$q^*(\\pi)$视为狄利克雷分布:\n",
    "$$ q^*(\\pi)=Dir(\\pi|\\alpha)$$\n",
    "接着利用概率乘积规则:\n",
    "$$\\begin{align}q^*(\\mu_k,\\Lambda_k)&=q^*(\\mu_k|\\Lambda_K)q^*(\\mu_k,\\Lambda_k)\\\\&=\\mathcal N(\\mu_k|m_k,(\\beta_k\\Lambda_k)^{-1})\\mathcal W(\\lambda_k|W_k,\\nu_k)\\end{align}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "更新⽅程类似于混合⾼斯模型的最⼤似然解的EM算法的M步骤的⽅程。\n",
    "* E-step:计算表示责任的期望$\\mathbb E[z_{nk}]=r_{nk}$\n",
    "  * $$ln \\tilde\\pi_k=\\mathbb E[ln\\pi_k]=\\psi(a_k)-\\psi(\\hat a)$$\n",
    "  * $$ln\\tilde\\Lambda_k=E[ln|\\Lambda_k|]=\\sum_{i=1}^D\\psi(\\frac{\\nu_k+1-i}{2}+Dln2+ln|W_k|$$\n",
    "  * $$r_{nk}\\propto \\tilde\\pi_k\\tilde\\Lambda_k^{\\frac{1}{2}}exp\\bigg\\{-\\frac{D}{2\\beta_k}-\\frac{\\nu_k}{2}(x_n-m_k)^TW_k(x_n-m_k)\\bigg\\}$$\n",
    "* M-step:令责任不变，重新计算各变分分布的参数\n",
    "   * $$N_K=\\sum_{n=1}^Nr_{nk}$$\n",
    "   * $$ \\overline x_k=\\frac{1}{N_k}\\sum_{n=1}^{N}r_{nk}x_N$$\n",
    "   * $$S_k=\\frac{1}{N_k}\\sum_{n=1}^Nr_{nk}(x_n-\\overline x_k)(x_n-\\overline x_k)^T$$\n",
    "   * $$\\alpha_k=\\alpha_0+N_K$$\n",
    "   * $$\\beta_k=\\beta_O+N_k$$\n",
    "   * $$m_k=\\frac{1}{\\beta_k}(\\beta_0m_0+N_k\\overline x_k)$$\n",
    "   * $$ W_k^{-1}=W^{-1}_0+N_KS_K+\\frac{\\beta_0N_K}{\\beta_0+N_K}(\\overline x_k-m_0)(\\overline x_k-m_0)^T$$\n",
    "   * $$\\nu_k=\\nu_0+N_k$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "后验概率分布中的混合系数的期望值为\n",
    "$$\\mathbb E[\\pi_k]=\\frac{\\alpha_0+N_k}{K\\alpha_0+N}$$\n",
    "* 当$\\alpha_0 \\rightarrow 0$时，分量$\\mathbb E[\\pi_k] \\rightarrow 0$，对模型不起作用\n",
    "* 当$\\alpha_0 \\rightarrow \\infty$时,分量$\\mathbb E[\\pi_k] \\rightarrow \\frac{1}{K}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "变分⽅法使得我们可以在确定混合分布中分量的最优数量时不必借助于交叉验证的技术,因为混合系数$\\pi$的狄利克雷分布在$\\alpha$小于1时倾向于选择接近0的值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "#sys.path\n",
    "sys.path.append(\"../\")\n",
    "import matplotlib.animation as animation\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "from prml.rv import VariationalGaussianMixture\n",
    "from prml.features import PolynomialFeatures\n",
    "from prml.linear import (\n",
    "    VariationalLinearRegressor,\n",
    "    VariationalLogisticRegressor\n",
    ")\n",
    "\n",
    "np.random.seed(666)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = np.random.normal(size=(100, 2))\n",
    "x1 += np.array([-5, -5])\n",
    "x2 = np.random.normal(size=(100, 2))\n",
    "x2 += np.array([5, -5])\n",
    "x3 = np.random.normal(size=(100, 2))\n",
    "x3 += np.array([0, 5])\n",
    "x_train = np.vstack((x1, x2, x3))\n",
    "\n",
    "x0, x1 = np.meshgrid(np.linspace(-10, 10, 100), np.linspace(-10, 10, 100))\n",
    "x = np.array([x0, x1]).reshape(2, -1).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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FEjlrKwbvIXcMO/disJrJi49hzcqddOjcsMo1GH7TmUz/YCYfPzqRvhf2OKo1HYT4X8m/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efce5d45048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,6))\n",
    "vgmm = VariationalGaussianMixture(n_components=6)\n",
    "vgmm.fit(x_train)\n",
    "\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=vgmm.classify(x_train))\n",
    "plt.contour(x0, x1, vgmm.pdf(x).reshape(100, 100))\n",
    "plt.xlim(-10, 10, 100)\n",
    "plt.ylim(-10, 10, 100)\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.ArtistAnimation at 0x7efce2584b00>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vgmm = VariationalGaussianMixture(n_components=6)\n",
    "vgmm._init_params(x_train)\n",
    "params = np.hstack([param.flatten() for param in vgmm.get_params()])\n",
    "fig = plt.figure(figsize=(6,6))\n",
    "colors = np.array([\"r\", \"orange\", \"y\", \"g\", \"b\", \"purple\"])\n",
    "frames = []\n",
    "for _ in range(100):\n",
    "    plt.xlim(-10, 10)\n",
    "    plt.ylim(-10, 10)\n",
    "    plt.gca().set_aspect('equal', adjustable='box')\n",
    "    r = vgmm._variational_expectation(x_train)\n",
    "    imgs = [plt.scatter(x_train[:, 0], x_train[:, 1], c=colors[np.argmax(r, -1)])]\n",
    "    for i in range(vgmm.n_components):\n",
    "        if vgmm.component_size[i] > 1:\n",
    "            imgs.append(plt.scatter(vgmm.mu[i, 0], vgmm.mu[i, 1], 100, colors[i], \"X\", lw=2, edgecolors=\"white\"))\n",
    "    frames.append(imgs)\n",
    "    vgmm._variational_maximization(x_train, r)\n",
    "    new_params = np.hstack([param.flatten() for param in vgmm.get_params()])\n",
    "    if np.allclose(new_params, params):\n",
    "        break\n",
    "    else:\n",
    "        params = np.copy(new_params)\n",
    "plt.close()\n",
    "plt.rcParams['animation.html'] = 'html5'\n",
    "anim = animation.ArtistAnimation(fig, frames)\n",
    "anim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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